An equation of state is derived which has promise for the prediction of high-density fluid behavior. An approximate form of this new equation yields expressions for approximate virial coefficients of all orders as functions of lower-order exact virial coefficients. Use of only the exact second and third virial coefficients in the second-order approximate equation leads to accurate prediction of rigid-sphere fluid behavior at high densities where even the fourth-order virial equation fails. For real fluids, the second-order approximate equation is accurate to high densities for temperatures above the Boyle temperature. At moderately lower temperatures, the third-order approximate equation yields accurate predictions at high densities where the third-order virial equation is in error.